Properties

Level $36$
Weight $0$
Character 36.1
Symmetry even
Fricke sign $-1$

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Maass form invariants

Level: \( 36 = 2^{2} \cdot 3^{2} \)
Weight: \( 0 \)
Character: 36.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \( 5.81501547383 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=+0.000000000\) \(a_{4}=+0.000000000\) \(a_{5}=-0.606433471\)
\(a_{6}=+0.000000000\) \(a_{7}=+0.649556872\) \(a_{8}=+0.000000000\) \(a_{9}=+0.000000000\) \(a_{10}=+0.000000000\)
\(a_{11}=+1.011126643\) \(a_{12}=+0.000000000\) \(a_{13}=-0.561089348\) \(a_{14}=+0.000000000\) \(a_{15}=+0.000000000\)
\(a_{16}=+0.000000000\) \(a_{17}=-1.074535350\) \(a_{18}=+0.000000000\) \(a_{19}=+1.082317357\) \(a_{20}=+0.000000000\)
\(a_{21}=+0.000000000\) \(a_{22}=+0.000000000\) \(a_{23}=-1.924198167\) \(a_{24}=+0.000000000\) \(a_{25}=-0.632238446\)
\(a_{26}=+0.000000000\) \(a_{27}=+0.000000000\) \(a_{28}=+0.000000000\) \(a_{29}=-1.613106833\) \(a_{30}=+0.000000000\)
\(a_{31}=-0.857183831\) \(a_{32}=+0.000000000\) \(a_{33}=+0.000000000\) \(a_{34}=+0.000000000\) \(a_{35}=-0.393913028\)
\(a_{36}=+0.000000000\) \(a_{37}=+0.525607662\) \(a_{38}=+0.000000000\) \(a_{39}=+0.000000000\) \(a_{40}=+0.000000000\)
\(a_{41}=-1.208128013\) \(a_{42}=+0.000000000\) \(a_{43}=+1.489697640\) \(a_{44}=+0.000000000\) \(a_{45}=+0.000000000\)
\(a_{46}=+0.000000000\) \(a_{47}=+0.407222356\) \(a_{48}=+0.000000000\) \(a_{49}=-0.578075870\) \(a_{50}=+0.000000000\)
\(a_{51}=+0.000000000\) \(a_{52}=+0.000000000\) \(a_{53}=-0.356323284\) \(a_{54}=+0.000000000\) \(a_{55}=-0.613181039\)
\(a_{56}=+0.000000000\) \(a_{57}=+0.000000000\) \(a_{58}=+0.000000000\) \(a_{59}=-0.386468353\) \(a_{60}=+0.000000000\)
\(a_{61}=-0.936000445\) \(a_{62}=+0.000000000\) \(a_{63}=+0.000000000\) \(a_{64}=+0.000000000\) \(a_{65}=+0.340263360\)
\(a_{66}=+0.000000000\) \(a_{67}=-0.530331772\) \(a_{68}=+0.000000000\) \(a_{69}=+0.000000000\) \(a_{70}=+0.000000000\)
\(a_{71}=-0.240602367\) \(a_{72}=+0.000000000\) \(a_{73}=+1.533792611\) \(a_{74}=+0.000000000\) \(a_{75}=+0.000000000\)
\(a_{76}=+0.000000000\) \(a_{77}=+0.656784259\) \(a_{78}=+0.000000000\) \(a_{79}=+0.651081225\) \(a_{80}=+0.000000000\)
\(a_{81}=+0.000000000\) \(a_{82}=+0.000000000\) \(a_{83}=-1.663677020\) \(a_{84}=+0.000000000\) \(a_{85}=+0.651634201\)
\(a_{86}=+0.000000000\) \(a_{87}=+0.000000000\) \(a_{88}=+0.000000000\) \(a_{89}=+1.761912315\) \(a_{90}=+0.000000000\)
\(a_{91}=-0.364459441\) \(a_{92}=+0.000000000\) \(a_{93}=+0.000000000\) \(a_{94}=+0.000000000\) \(a_{95}=-0.656353472\)
\(a_{96}=+0.000000000\) \(a_{97}=-0.422521195\) \(a_{98}=+0.000000000\) \(a_{99}=+0.000000000\) \(a_{100}=+0.000000000\)

Showing 100 of 352 available coefficients

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